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Integrable Classical and Quantum Gravity


Nicolai,  Hermann
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Nicolai, H., Korotkin, D. A., & Samtleben, H. (2006). Integrable Classical and Quantum Gravity. NATO Advanced Study Institute on Quantum Fields and Quantum Space Time. Cargese, France, 2006-07-22 - 2006-08-03.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-4A4E-F
In these lectures we report recent work on the exact quantization of dimensionally reduced gravity, i.e. 2d non-linear (G/H)-coset space sigma-models coupled to gravity and a dilaton. Using methods developed in the context of flat space integrable systems, the Wheeler-DeWitt equations for these models can be reduced to a modified version of the Knizhnik-Zamolodchikov equations from conformal field theory, the insertions given by singularities in the spectral parameter plane. This basic result in principle permits the explicit construction of solutions, i.e. physical states of the quantized theory. In this way, we arrive at integrable models of quantum gravity with infinitely many self-interacting propagating degrees of freedom.